Driven by the fast proliferation of Internet of Things (IoT), massive machine-type communication (mMTC) has been identified as one of the main use cases of the sixth-generation (6G) wireless networks [1]}-[2]}. Generally speaking, mMTC has three fundamental characteristics, namely massive connectivity, sporadic data traffic and small payload [3]}. In the context of mMTC, conventional grant-based random access schemes lead to a high access latency and a prohibitive signaling overhead. To this end, grant-free random access schemes have been regarded as a candidate technology of 6G wireless networks [4]}, [5]}. In particular, active devices transmit their data signals without a grant from the BS after sending pre-assigned pilot sequences. Hence, the key of grant-free random access is active device detection and channel estimation at the BS based on the received pilot sequences.
